Depends if you're customer facing or not and many other factors related to job function. If you walk in a HP office you will find everything from business suits to jeans (mainly because HP supports many business functions out of a single location.) For the most part, when meeting internally but at official functions you will find business casual.
There are many internal groups/societies within HP based on common interests. Everything from philanthropy to community outreach to hiking to advanced physics. There is a tremendous emphasis within the company on being green as we have a significant impact on our environment.
A typical day is working until you get the job done. I would say your priorities are your customer, your job, the company, and you.